The City midfielder was sent to hospital for scans on the arm injury he sustained in the 1-1 draw with The Foxes at Ashton gate on Tuesday night and was told he had not broken any bones.
"It's great news because we can't afford another long-term injury," Johnson told the club's official website.
"We've already got Jamal Campbell-Rice, Evander Sno and Jamie McAllister on the sidelines so everyone's pleased that Cole hasn't suffered a break."